The IIM Ahmebada Interview Question
"At 3:15, what is the angle between the hour hand and the minute hand of a clock?"
Let's find the angle.
Let' Understand the concept of angles
Before starting into addressing clock angle problems, it's important to understand how a clock performs geometrically. A clock is a circle, which means it has 360 degrees in total. To find the angle between the hour and minute hands at a given time, we must know:
- There are 12 hours, so each hour mark is 30 degrees apart (360° ÷ 12).
- The minute hand moves 6 degrees per minute (360° ÷ 60).
- The hour hand moves 0.5 degrees per minute (30° ÷ 60).
Here is the Step- By -Step solution of the interview question
So the given is Time: 3:15.
Step 1 - Lets find the Minute Hand Position first:
At 15 minutes, the minute hand is at:
15 minutes × 6° = 90 degrees
Step 2. Let's now find the Hour Hand Position
At exactly 3:00, the hour hand is at:
3 hours × 30° = 90 degrees
But at 3:15, the hour hand has moved ahead:
15 minutes × 0.5° = 7.5 degrees
So, total hour hand position = 90 + 7.5 = 97.5 degrees
Angle Between the Hands. Now, take the difference between the two positions:
|97.5° - 90°| = 7.5 degrees
What is the Final Answer?
The angle between the hour hand and the minute hand of a clock is 7.5 Degrees.
Why this question is considered as a tricky question?
During interviews the candidates must be stressed, and the answers given that time might not be calculated correctly. Many candidates quickly conclude that the hands are at a straight angle (90°) since it is quarter past 3. They forget that the hour hand advances gradually rather than only at every hour mark.
IIM interviewers primarily ask these types of questions to assess a candidate's attention to detail under pressure, rather than focussing on formulas.